Four Colour Theorem - English Dictionary english to english dictionary containing references. http://www.online-dictionary.biz/english/vocabulary/reference/four_colour_theore
Extractions: If you can't find the translation you need, try our free translation 1. four colour theorem four colour map theorem Fourier transform A technique for expressing a waveform as a weighted sum of sines and cosines. Computers generally rely on the version known as discrete Fourier transform. Named after J. B. Joseph Fourier 1768 1830. See also wavelet, discrete cosine transform. 1997-03-9 fourth generation computer A computer built using Very Large Scale Integration VLSI integrated circuits, especially a microcomputer based on a microprocesseor, or a parallel processor containing two to thousands of CPUs. VLSI made it routine to fabricate an entire CPU, main memory, or similar device with a single integrated circuit that can be mass produced at very low cost. This has resulted in new classes of machines such as personal computers, and high performance parallel processors that contains thousands of CPUs.
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Extractions: Higher resolution THE FOUR COLOUR THEOREM In Greek mythology, the Sirens were sisters whose song lured sailors to their deaths on a treacherous reef. The Four Colour Theorem is to mathematicians what the song of the Sirens was to the sailors of ancient times. Many a mathematician has foundered in attempting its proof . The problem is deceptively simple. Take a map of the world, a few coloured pens and start colouring in the countries. There's one ruleadjacent countries cannot be the same colour. The Four Colour Theorem is the hypothesis that the maximum number of colours needed to fill the map is four. It's the kind of problem that, for a mathematician, has the smell of simplicity and elegance about it. You just know that somebody somewhere will have come up with an elegant method that makes the answer apparent. Except they haven't. In place of an elegant proof is a monstrous machine created by Kenneth Appel and Wolfgang Haken, both mathematicians at the University of Illinois, who cracked the problem in 1976. But instead of insight and panache, they used force. Appel and Haken first worked out that they could reduce the number of possible maps from infinity to just 1,936. They then checked each one against the theory. The task turned out to be so intensive that they needed a computer to do it. Even then, it took hundreds of hours. In a sense, they squeezed the life out of the problem until it gave up its answer, a method known as brute force.
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Re: Artificial Intelligence computer program to verify the proof provided by the first one (and yes, it checks out). See http//en.wikipedia.org/wiki/four_colour_theorem Oliver http://coding.derkeiler.com/Archive/Java/comp.lang.java.help/2005-09/msg00718.ht
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Extractions: sci.math Top All Lists Date Enter your search terms Submit search form Web www.archivum.info Thread from [ boson boss Subject Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member From "boson boss" < Date 13 Feb 2006 16:45:29 -0800 Newsgroups sci.math sci.logic sci.physics http://www.justinmullins.com/four_colour_theorem.htm ... More with this subject... Current Thread Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member (continued) Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member Proginoskes Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member bill Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member boson boss Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member Proginoskes Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member ldb Re: proving Kepler Packing and 4 Color Mapping using the same technique of Smallest Member Proginoskes
Four Colour Theorem McFLY. Title page. four colour theorem. REDIRECT Four color theorem. The McFLY Encyclopedia is based on Wikipedia. See McFly copyrights for more info. http://en.mcfly.org/four_colour_theorem
Extractions: Computer Dictionary (Redirected from Computer Dictionary/four colour theorem Jump to: navigation search Position: Main Page Network Category Computer Dictionary Content: (Or "four colour theorem") The theorem stating that if the plane is divided into connected regions which are to be coloured so that no two adjacent regions have the same colour (as when colouring countries on a map of the world), it is never necessary to use more than four colours. The proof, due to Appel and Haken, attained notoriety by using a computer to check tens of thousands of cases and is thus not humanly checkable, even in principle. Some thought that this brought the philosophical status of the proof into doubt. There are now rumours of a simpler proof, not requiring the use of a computer. See also chromatic number Interaction Error Correction Recommendation Information ... More Search Using Google to search inside this website â Computer Dictionary/four colour map theorem â and outside this website â Computer Dictionary/four colour map theorem Retrieved from " http://en.18dao.net/Computer_Dictionary/four_colour_map_theorem
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Four Color Theorem Example of a fourcolored map. Example of a four-colored map. The four color theorem (also known as the four color map theorem) states that given any plane http://hanzi.1bx.com/en/Four_colour_theorem.htm
Extractions: Four color theorem Example of a four-colored map The four color theorem (also known as the four color map theorem ) states that given any plane separated into regions, such as a political map of the states of a country, the regions may be colored using no more than four colors in such a way that no two adjacent regions receive the same color. Two regions are called adjacent only if they share a border segment, not just a point. Each region must be contiguous : that is, it may not have exclaves like some real countries such as Angola Azerbaijan , the United States , or Russia It is often the case that using only three colors is inadequate. This applies already to the map with one region surrounded by three other regions (although with an even number of surrounding countries three colors are enough) and it is not at all difficult to prove that five colors are sufficient to color a map. The four color theorem was the first major theorem to be proven using a computer, and the proof is not accepted by all mathematicians because it would be unfeasible for a human to verify by hand (see computer-assisted proof ). Ultimately, in order to believe the proof, one has to have faith in the correctness of the
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